Problem:

const [textareaValue, setTextareaValue] = useState(props.currentMarkdown);

useState will use props.currentMarkdown as the initial value but it doesn't update the current state when props.currentMarkdown changes.

Unrelated:

The debounce update of the parent state can be improved by using useRef

const timeout = useRef();

const handleMarkdownChange = (newValue) => {
    if (timeout.current) {
        clearTimeout(timeout.current);
    }
    timeout.current = setTimeout(function () {
        console.log("fire");
        const items = [];
        for (let value of currentData.items) {
            if (value["id"] === currentData.active) {
                value.markdown = newValue;
                value.unsaved = true;
            }
            items.push(value);
        }
        setCurrentData({ ...currentData, items: items });
    }, 200);
};

using var timeout is bad because it declares timeout on every render, whereas useRef gives us a mutable reference that is persisted across renders